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Estimating CAPM Inputs Where do r f, Beta, and T C Come From?

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Estimating Betas Comparable firm or industry method –Regress rates of return on common stock against the rates of return on a “market” index. Normally we try to reduce the noise in betas by calculating industry betas. –This is simply the average of all of the equity betas for firms within the industry.

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Estimation Details Daily, weekly, monthly or annual returns? –In the ideal world of the CAPM, without transactions costs, it does not matter. –In the real world with bid-ask spreads it does. Investors buy stocks at the ask and sell them at the bid. The difference is the bid-ask spread and allows the market maker to earn a living. –Even absent any movement in a stock’s value, its price may change from day to day as the reported closing transaction bounces from the bid to the ask. –Bid-ask bounce makes it appear that movements in a stock are unrelated to the market. –Monthly returns minimize the impact of bid-ask bounce. If your data set is to short to use monthly returns go to weekly. If it is too short for that... Best of luck.

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More Estimation Details –What time period? Try to use 60 periods of data. Yes, that would be five years of monthly data. –Are dividends and rights included in rates of return? The holding period return should include ALL cash flows. If you can spend it, you should include it. –The initial cash outflow is the purchase price. –The final cash inflow is the sales price.

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The Final Estimation Details Which is the correct market index? –The CAPM market index includes all risky assets. In theory this means you want the index of everything. In practice this index does not exist. Even if it did you cannot own it as it includes items like real estate (your house), and human capital (you). –Wilshire 5000 comes close (^DWC). –CRSP index is similar (posted on the class web page) and includes all stocks on the NASDAQ, AMEX, and NYSE.

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One Final Beta Estimator Old joke: All betas equal one plus or minus estimation error. –There is a lot of truth to this crack. –Out of sample firms with low beta estimates tend to have unexpectedly high return correlations with the market. The reverse is true too. –On average betas have to equal one. Why not use this value absent convincing evidence to the contrary?

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The Risk Free Rate No Easy Answers Technical answer. –The mathematical models used to generate the intertemporal CAPM includes a risk free asset that pays an instantaneous interest rate r f. –Based on this you want the interest rate on a short dated treasury instrument. –But, these are stationary models. Things like inflation are not expected to change over time. –Still there is evidence that this is your best estimate of the long run risk free rate. Out of sample economic models do a very poor job of predicting interest rates. Best model is typically that next year’s rate will equal this year’s rate.

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Risk Free Rate Continued Intuitive Answer –Use a ten year treasury rate. Allows for changing returns over time. –Problems Return from holding short dated government bonds over ten years. Think of buying one year bonds every year for ten years. Return from holding a single ten year bond. Single ten year bond has on average a higher return. This means the long dated bond returns include a risk premium. We want the risk free rate. –Partial solution: subtract out the historical risk premium of about 1%.

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Risk Free Rate Continued Not intuitive and not easy answer. –Calculate the forward rates from government bonds. Use these forward rates as your risk free rate. –Good Allows for time variation in interest rates. –Bad Forward rates more than a year out are likely to include a risk premium. Pain in the neck to do this, often with only a minor impact to the final calculated value. –One of Many Possible Compromises Use the five year bond’s return for your projected cash flows. Use the ten year bond’s return for your terminal value’s cash flows.

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Market Risk Premium Another difficult and controversial topic. –The argument for 4%. Given today’s market, and the historical growth in GDP it is hard to imagine a world in which stocks return more than 4% forever. –The argument for 7%. This is the historical value. The 4% argument could have been made many times in the past. It has yet to describe the market. –The argument for values in between. I hate fighting, how about we all compromise on...

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Estimating r D and β D Just how accurate a number do you need? –Not very? Use either: Last year’s interest payments divided by the outstanding debt. The current yield to maturity its debt. Set β D to zero. What can go wrong? –How risky is the debt? Not very? Then not much. Use one of the above estimates.

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Estimating r D No public debt? Call the bank! –Alternatively, go to their financial statements and use the interest paid divided by the outstanding debt. With public debt. –Start with the yield to maturity of the bonds. –Adjust this for the chance the company will default on the bonds. Use historical estimates to do the adjustment.

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Risky Debt The firm’s debt is very risky? –If there is a reasonable chance the firm will default then the interest rate on the firm’s debt will overestimate r D. –Investors will demand a higher promised yield to compensate them for those times when the firm fails to pay in full. –β D will have the same sign as β A.

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How Risky is Risky? Bond Ratings Major rating agencies: –Moody’s –S&P –Fitch General categories –Investment grade (a.k.a. high grade) BBB rating and higher. –High yield (a.k.a. junk) Not investment grade, and not in default. –Distressed In default

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Historical Bond Returns and Yields Averages for 1989-2003 ML 5-10 Yr Treasury Yld ML 5-10 Yr Treasury TR ML 10-15 Yr Treasury Yld ML 10-15 Yr Treasury TR LB AAA Corp Yld LB AAA Corp TR 6.078.916.889.586.598.96 ML BB Hi-Yld Yld ML BB Hi- Yld TR ML B Hi-Yld Yld ML B Hi-Yld TR LB CCC Hi-Yld Yld LB CCC Hi-Yld TR 9.389.7811.779.7118.5310.12 ML 1-5 Yr C Rated Hi-Yld Yld ML 1-5 Yr C Rated Hi- Yld TR 21.9314.19 Key: ML = Merrill Lynch, LB = Lehman Brothers, Yld = Yield to Maturity, TR = Total Return

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Items to Note Yield and total return are not the same thing! –Question: Why is the total return on treasuries higher than the yield? –Question: Why is this relationship reversed for CCC bonds? The lower the corporate bond class rating the higher the yield. The lower the corporate bond class rating the sometimes higher, sometimes lower the total return. A table with the year by year data is on the class web page.

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Adjusting r D for Default Risk The return on the firm’s debt is equivalent the total return in the table. Problem: You have yield to maturity data not expected return data. One possible solution: Adjust the YTM using the historical relationship between YTM and r D based on the firm’s debt’s rating class.

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A Warning The data on the web page is from 1989- 2003, which includes a very long economic boom. –During booms high yield debt should produce a return higher than investors expected. –During busts the opposite is true. Are the 1989-2003 averages reflective of what investors expected?

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Long Run Bond Returns December 1926 – December 1989 Treasury Yld (4-4.99 yrs) Treasury TR (4-4.99 yrs) Treasury Yld (5-9.99 yrs) Treasury TR (5-9.99 yrs) Avg.6.496.61 6.35 AA YldAA TRBAA YldBAA TR Avg.7.595.868.466.82 Key: Yld = Yield to Maturity, TR = Total Return

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Long Run Results Contrasts with data from 1989-2003 –For the long run data the AA and BAA bonds have higher YTM’s than TR’s. As expected. –For the 1989-2003 data the AA and BAA bonds have lower YTM’s than TR’s. Probably due to the long economic boom. –Lower credit quality bonds have higher total returns. Another item to note: AA TR’s have been lower than government TR’s! Very odd. The underlying data for the long run table is on the class web page.

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Estimating T C Use the average U.S. combined federal and state rate of 40%. Use the value management provides. Matt’s never before seen method!

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Average U.S. Combined Rate The average combined federal and state tax rate is 40%. –Good for primarily domestic firms that have been profitable. –Good long run value for firms you believe will become profitable. –Bad for firms with current or recent losses that may have tax loss carry forwards. –Potentially bad for firms with large foreign operations or overseas “headquarters.”

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Management’s Reported Value In the firm’s financial reports management will often provide their firm’s tax rate for the previous period. –This is often calculated as: 1- Net Income After Taxes/Net Income Before Taxes.

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Management Reports: Good and Bad Often accurate since management has access to the proprietary information provided to the IRS for calculating their taxes. Good: Net Income numbers may provide an accurate picture of the marginal tax rate. Bad: Net Income numbers are not cash flows and may not reflect the firm’s marginal or even average tax rate. May not reflect future tax rates for firm’s that have been unprofitable but are now becoming profitable.

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Matt’s Never Seen Before Method Calculate the annual tax rate as the Cash Taxes Paid/FCF Before Taxes. Use the average of the above from at least five years of data.

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Matt’s Method: Good and Bad Good: Uses only cash flow numbers. Good: Over the “long run” this is the fraction of the firm’s free cash flow the government keeps. –Theoretically the number you want if this is the expected marginal tax rate going forward. Bad: Very volatile. Tax rates will appear to jump dramatically from year to year. –Averaging helps quite a bit but with only five to ten data points perhaps not enough. Bad: May not reflect future tax rates for firm’s that have been unprofitable but are now becoming profitable.

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Combining the Best of All Methods Goal: Obtain the firm’s tax rate in the years ahead. Problem: Must use past data. Solution: Project based on trends. –Recently unprofitable firms will have relatively low tax rates for at least the next few years as they use up their tax loss carry forwards. Once a firm uses up its tax loss carry forwards expect its tax rate to approach 40% or its industry average. –Recently profitable firms will likely have the same tax rate going forward.

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